Lab 2: Star Counts
How many stars
can you see? People say that some really big number is “more than the stars in
the sky,” but how many is that? In this lab you will make an estimate of how
many stars you could see if you could see the entire sky with your naked eye and
how many stars you could see using your telescope. It would not be possible to
count all the stars visible in the sky during a single lab meeting. For one
reason, the number is very large; for another, only half the sky is visible at
any given time. So what you will do is to count the stars visible in a small
area of the sky and then multiply your count by the number of those areas it
would take to cover the entire sky. You will then make similar measurements
through the low-power eyepiece of your telescope.
Knowing how many
stars you can see will allow you to find the limiting magnitude visible
to you. The limiting magnitude is the magnitude of the dimmest stars visible.
(Magnitude is the numerical value given to the measure of a star’s
brightness; you will hear more about this at lab. Larger numbers mean dimmer stars. From a very dark, clear site most
people have a limiting magnitude of about 6.)
Here’s the basic
procedure. You will be given a paper roll of known length and radius. You will
look through this roll at several random patches of sky and count the number of
stars you can see. Then you will average those star counts to get an average
number of stars visible through the roll. Then you will multiply it by the
number of those patches it would take to cover the sky. That will tell you the
number of stars visible to the naked eye. Then you will repeat that with your
low power eyepiece and telescope to find the number of stars visible through the
telescope.
The challenging
part of this lab is to figure out the number of patches of sky visible through
your roll or telescope it would take to cover the sky. Here’s how it works.
The first item is what is meant by a “square degree.” Imagine an area on the
sky that is a square 1° by 1°. That area is one square degree or 1 sq deg. To
cover the entire sky would take approximately 41,253 of these squares, so the
entire sky has an area of 41,253 sq deg. The view through your rolls has an
area of 130 sq deg, so the number of patches of roll it would take to cover the
sky is 41,253/130 or 316. Call this number Mr, to stand for the
multiplying number for the roll. Multiplying Mr by the average number of
stars you see through the roll will give you the number of stars visible to the
naked eye. For the telescope, it’s a bit more challenging. The area you see
through the eyepiece is a circle, so the area in square degrees is πR2
where R is the radius of the field of your eyepiece (measured in
degrees). In a previous lab the diameter of the field of view for the
low power eyepiece was found to be 60.0’ or 1.00°. You will need to halve that
to get R = 0.500°; the value of π is probably on your calculator, or you can use
3.14 to approximate π. With R and π, calculate πR2 to be 0.7854 and
divide that into 41,253 to get the number of patches of telescope it
would take to cover the sky; call this number Mt. Mt =
41253/0.7854 = 52,500. Multiplying Mt by the average number of stars you
see through the eyepiece of the scope will give you the number of stars visible
through the telescope.
Materials
Telescope and eyepieces,
viewing roll, calculator, telescope setup instructions from Lab 1
Procedure
 | Read through this entire
write up carefully before coming to lab. |
| Hold the roll against
your eye and view a region of the sky over halfway up from the horizon.
 | Pick your region
randomly; don’t attempt to aim it at a particular spot. |
| If there are no stars
visible, do not shift to another region. Simply record 0 for the
number of stars visible. |
|
| Make a total of 8 star
counts through the viewing roll (4 by you and 4 by your partner). |
| Record each of these star
counts. (You’ll do the calculations later.) |
| Set up and align the
telescope per the instructions given in Lab 1. Polar alignment is not
critical for this lab. |
| Install the low power
eyepiece and focus carefully. |
| Randomly point the
telescope at a region of sky over halfway up from the horizon and count
the number of stars you can see. Record your count. |
| Repeat this for a total
of 5 regions of sky. |
| Return your equipment.
You may do your calculations at home or during the time remaining in lab. |
| Calculate the number of
stars visible to the naked eye by:
| Averaging your 8 star
counts. (Include any decimal places in your average.) |
| Multiplying this average
by Mr to get the number of stars visible to the naked eye. |
|
| Calculate the number of
stars visible through the telescope by:
| Averaging your 5 star
counts. (Include any decimal places in your average.) |
| Multiplying your average
star count by Mt to get the number of stars visible through the
telescope. |
|